Obtaining true diffusivity constant

ABSTRACT

The subject disclosure presents systems and computer-implemented methods for calculating the diffusivity constant of a sample using acoustic time-of-flight (TOF) based information correlated with a diffusion model to reconstruct a sample&#39;s diffusivity coefficient. Operations disclosed herein such as acoustically determining the phase differential accumulated through passive fluid exchange (i.e. diffusion) based on the geometry of the tissue sample, modeling the impact of the diffusion on the TOF, and using a post-processing algorithm to correlate the results to determine the diffusivity constant, are enabled by monitoring the changes in the speed of sound caused by penetration of fixative such as formalin into several tissue samples. A tissue preparation system may be adapted to monitor said diffusion of a tissue sample and determine an optimal processing workflow.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.15/624,644 filed on Jun. 15, 2017, which application is a continuationof International Patent Application No. PCT/EP2015/080251 filed Dec. 17,2015, which applications claims priority to and the benefit of U.S.Provisional Patent Application No. 62/093,151, filed Dec. 17, 2014, thedisclosures of which are hereby incorporated by reference herein intheir entireties.

BACKGROUND OF THE SUBJECT DISCLOSURE Field of the Subject Disclosure

The present subject disclosure relates to analysis of materials such astissue samples. More particularly, the present subject disclosurerelates to calculating a true diffusivity constant for a material.

Background of the Subject Disclosure

Measuring the diffusivity constant (i.e. diffusivity coefficient) isimportant to multiple areas of basic and applied science because itrepresents a fundamental property of fluids and solids and therefore hasdirect application to a number of commercial fields. For instance, thediagnostic value of the diffusivity coefficient has proven useful indistinguishing normal versus abnormal tissue. In immunohistochemistry(IHC) imaging, biological specimens such as tissue sections from humansubjects are often placed in a liquid or fixative that will suspend themetabolic activities of the cells. Monitoring diffusion of fixativesthrough a tissue sample is useful for determining whether the fixativehas infused the entire tissue sample, thereby minimizing or limitingunder-fixed tissue or over-fixed tissue.

Several methods for calculating the diffusivity constant have beenpresented in prior art including magnetic resonance imaging (MRI)diffusion weighted imaging, electrolyte monitoring of a fluid, opticaldetection and quantification, and x-ray based methods. Of thesetechniques, MRI-based methods are by far the most common clinically usedmethod. However, each of these methods has its own limitations in termsof detection, sensitivity, cost, complexity, sample compatibility, andrequired acquisition time. Electrolyte monitoring-based methods requireactive diffusion of electrically different materials, meaning thatelectrically-neutral materials cannot be monitored with this method. Themajor drawback of optical techniques is that they mainly produce arelative representation of the diffusion coefficient that is typicallyrelated back to known standard. That can make absolute quantification ofthe diffusivity constant difficult. As noted earlier, much work has beendone using MRI to detect and quantify the diffusivity coefficient.However, this is derived from the detection of the nuclear magnetizationof mobile water protons in the body. This makes MRI well-suited todetect and monitor water diffusion although the modality currently haslimited utility in monitoring the diffusion of other alternate fluids.

SUMMARY OF THE SUBJECT DISCLOSURE

The subject disclosure solves the above-identified problems bypresenting systems and computer-implemented methods for calculating thediffusivity constant of a sample using acoustic time-of-flight (TOF)based information correlated with a diffusion model to reconstruct asample's diffusivity coefficient. Operations disclosed herein such asacoustically determining the phase differential accumulated throughpassive fluid exchange (i.e. diffusion) based on the geometry of thetissue sample, modeling the impact of the diffusion on the TOF, andusing a post-processing algorithm to correlate the results to determinethe diffusivity constant, are enabled by monitoring the changes in thespeed of sound caused by penetration of fixative such as formalin intoseveral tissue samples. A tissue preparation system may be adapted tomonitor said diffusion of a tissue sample and determine an optimalprocessing workflow. Moreover, the disclosed operations are not limitedto solely quantifying water diffusion, but may be used to monitor thediffusion of all fluids into all tissues and other materials, unlike theprior art methods identified above.

In one exemplary embodiment, the subject disclosure provides a methodfor determining a true diffusivity constant for a sample immersed withina reagent, the method including simulating a spatial dependence of adiffusion into the sample over a plurality of time points and for eachof a plurality of candidate diffusivity constants to generate a modeltime-of-flight, and comparing the model time-of-flight with anexperimental time-of-flight to obtain an error function, wherein aminimum of the error function yields the true diffusivity constant.

In another exemplary embodiment, the subject disclosure provides asystem including an acoustic monitoring device that detects acousticwaves that have traveled through a tissue sample, and a computing devicecommunicatively coupled to the acoustic monitoring device, the computingdevice is configured to evaluate a speed of the acoustic waves based ona time of flight and including instructions, when executed, for causingthe processing system to perform operations comprising setting a rangeof candidate diffusivity constants for the tissue sample, simulating aspatial dependence of a reagent within the tissue sample for a pluralityof time points and for a first of the range of candidate diffusivitypoints, determining a modeled time-of-flight based on the spatialdependence, repeating the spatial dependence simulation for each of theplurality of diffusivity constants, and determining an error between themodeled-time-of-flight for the plurality of diffusivity constants versusan experimental time-of-flight for the tissue sample, wherein a minimumof an error function based on the error yields a true diffusivityconstant for the tissue sample.

In yet another exemplary embodiment, the subject disclosure provides atangible non-transitory computer-readable medium to storecomputer-readable code that is executed by a processor to performoperations including comparing a simulated time-of-flight for a samplematerial with an experimental time-of-flight for the sample material,and obtaining a diffusivity constant for the sample material based on aminimum of an error function between the simulated time-of-flight andthe acoustic time-of-flight.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a tissue processing system 100 for optimized tissuefixation, according to an exemplary embodiment of the subjectdisclosure.

FIGS. 2A and 2B respectively show depictions of ultrasound scan patternsfrom a biopsy capsule and from a standard-sized cassette, according toan exemplary embodiment of the subject disclosure.

FIG. 2C shows a timing diagram for an exemplary embodiment of thesubject disclosure.

FIG. 3 shows a method for obtaining a diffusivity coefficient for atissue sample, according to an exemplary embodiment of the subjectdisclosure.

FIG. 4 shows an alternate method for obtaining a diffusivity coefficientfor a tissue sample, according to an exemplary embodiment of the subjectdisclosure.

FIGS. 5A-5B respectively show a simulated concentration gradient for afirst time point, and for several time points over the course of anexperiment, according to an exemplary embodiment of the subjectdisclosure.

FIGS. 6A and 6B respectively depict plots of the simulated amount ofdetected concentration of NBF by the ultrasound over the course of theexperiment and the simulated TOF signal for the first candidatediffusivity constant, according to exemplary embodiments of the subjectdisclosure.

FIG. 7 depicts temporally varying TOF signals calculated for allpotential diffusivity constants, according to an exemplary embodiment ofthe subject disclosure.

FIGS. 8A and 8B respectively depict experimentally calculated TOF trendsand a spatially-averaged TOF signal collected from a 6 mm piece of humantonsil sample, according to an exemplary embodiment of the subjectdisclosure.

FIGS. 9A and 9B respectively show plots of the calculated error functionbetween simulated and experimentally measured TOF signals as a functionof candidate diffusivity constant and a zoomed-in view of the errorfunction.

FIG. 10 depicts a TOF trend calculated with a modeled diffusivityconstant plotted alongside an experimental TOF, according to anexemplary embodiment of the subject disclosure.

FIGS. 11A and 11B. FIG. 11A show reconstructed diffusivity constants forthe multiple tissue samples.

FIGS. 12A-12B show a system comprising a transmitter and a receiver pairfor measuring TOF via phase shifts.

DETAILED DESCRIPTION OF THE SUBJECT DISCLOSURE I. TechnicalImplementation

The subject disclosure solves the above-identified problems bypresenting systems and computer-implemented methods for calculating thediffusivity constant (also known as “diffusion coefficient”) of a sampleusing acoustic time-of-flight (TOF) based information correlated with adiffusion model to reconstruct a sample's diffusivity coefficient.Tissue preparation systems and methods disclosed herein may be adaptedto monitor the diffusion of fixative fluid into a tissue sample. Forexample, as formalin penetrates into tissue, it displaces interstitialfluid. This fluid exchange slightly changes the composition of thetissue volume because interstitial fluid and formalin have discretesound velocities. The output ultrasound pulse thus accumulates a smalltransit time differential that increases as more fluid exchange occurs.This enables operations such as determining the phase differentialaccumulated by diffusion based on the geometry of the tissue sample,modeling the impact of the diffusion on the TOF, and using apost-processing algorithm to correlate the results to determine thediffusivity constant. Moreover, the sensitivity of the disclosed TOFinstruments can detect a change of less than 10 parts per millionenabling potentially more accurate characterization of the diffusivityconstant. On the nanosecond TOF scale, all fluids and tissues will havediscrete sound velocities, so the disclosed operations are not limitedto solely quantifying water diffusion, but may be used to monitor thediffusion of all fluids into all tissues.

The rate of diffusion may be monitored by a system of acoustic probesbased on the different acoustic properties of formalin-soaked tissuesamples. Such a system for diffusion monitoring and experimental TOFmeasurement is described in further detail in commonly-assigned andco-pending U.S. Patent Publication 2013/0224791, in U.S. PatentApplications entitled MATERIALS AND METHODS FOR OPTIMIZED TISSUEFIXATION filed in December 2014, in U.S. Patent Applications entitledMATERIALS AND METHODS FOR STANDARDIZING DIFFUSION OF A FLUID INTOTISSUES filed in Feb. 9, 2015 and in U.S. Patent Application entitledDIFFUSION MONITORING PROTOCOL FOR OPTIMIZED TISSUE FIXATION filed inDec. 29, 2014, the contents of each of which are hereby incorporated byreference herein in their entirety. A suitable system for diffusionmonitoring and experimental TOF measurement is also described in theinternational patent application entitled ACCURATELY CALCULATINGACOUSTIC TIME-OF-FLIGHT filed in Dec. 17, 2015, the contents of each ofwhich are hereby incorporated by reference herein in their entirety. Thereferenced applications describe solid tissue samples being contactedwith a liquid fixative that travels through the tissue samples anddiffuses throughout substantially the entire thickness of the tissuesamples, and being analyzed based on acoustic characteristics that arecontinuously or periodically monitored to evaluate the state andcondition of the tissue sample throughout processing. For example, afixative such as formalin having a bulk modulus greater thaninterstitial fluid can significantly alter the ToF as it displaces theinterstitial fluid. Based on the obtained information, a fixationprotocol may be adjusted to enhance processing consistency, reduceprocessing times, improve processing quality, or the like. The acousticmeasurements may be used to non-invasively analyze tissue samples. Theacoustic properties of tissue samples may change as liquid reagent(e.g., a liquid fixative) travels through the sample. The sample'sacoustic properties can change during, for example, a pre-soak process(e.g., diffusion of cold fixative), a fixation process, a stainingprocess, or the like. In the fixation process (e.g., a cross-linkingprocess), the speed of transmission of acoustic energy can change as thetissue sample becomes more heavily cross-linked. Real-time monitoringcan be used to accurately track movement of the fixative through thesample. For example, a diffusion or fixation status of a biologicalsample can be monitored based on a time of flight (TOF) of acousticwaves. Other examples of measurements include acoustic signal amplitude,attenuation, scatter, absorption, phase shifts of acoustic waves, orcombinations thereof.

According to embodiment, the movement of the fixative through the tissuesample may be monitored in real-time.

II. Systems and Methods

A “time-of-flight” or “TOF” as used herein is, for example, the timethat it takes for an object, particle or acoustic, electromagnetic orother wave to travel a distance through a medium. The TOF may bemeasured empirically e.g. by determining a phase differential betweenthe phases of an acoustic signal emitted by a transmitter (“transmittedsignal”) and an acoustic signal received by a receiver (“receivedsignal”).

A “sample” as used herein is, for example, a biological specimencontaining multiple cells. Examples include, but are not limited to,tissue biopsy samples, surgical specimen samples, amniocentesis samplesand autopsy material. The samples may be contained e.g. on a tissuesample slide.

The “Porosity” is a measure of the void (i.e. “empty”) spaces in amaterial, and is a fraction of the volume of voids over the total volumeof an object, between 0 and 1, or as a percentage between 0 and 100%. A“porous material” as used herein is, for example, a 3D object whoseporosity is larger than 0.

A “diffusion coefficient” or “diffusivity constant” as used herein is,for example, a proportionality constant between the molar flux due tomolecular diffusion and the gradient in the concentration of the objectwhose diffusion is observed (or the driving force for diffusion).Diffusivity is encountered e.g. in Fick's law and numerous otherequations of physical chemistry. The higher the diffusivity (of onesubstance with respect to another), the faster they diffuse into eachother. Typically, a compound's diffusivity constant is ˜10,000× as greatin air as in water. Carbon dioxide in air has a diffusivity constant of16 mm2/s, and in water its diffusivity constant is 0.0016 mm2/s.

A “phase differential” as used herein is, for example, the difference,expressed in degrees or time, between two waves having the samefrequency and referenced to the same point in time.

A “biopsy capsule” as used herein is, for example, a container for abiopsy tissue sample. Typically, a biopsy capsule comprises a mesh forholding the sample and letting a liquid reagent, e.g. a buffer, afixation solution or a staining solution surround and diffuse into atissue sample. A “cassette” as used herein is, for example, a containerfor a biopsy capsule. Preferentially, the cassette is designed andshaped such that it can automatically be selected and moved, e.g.raised, relative to the beam path of an ultrasonic transmitter-receiverpair. The movement may be performed for example by a robotic arm oranother automated movable component of a device onto which the cassetteis loaded.

In an embodiment, a system of calculating a diffusion constant isprovided, said system comprising a signal analyzer containing aprocessor and a memory coupled to the processor, the memory to storecomputer-executable instructions that, when executed by the processor,cause the processor to perform operations including calculation of adiffusivity constant from a set of acoustic data as discussed in furtherdetail below.

A data input into the signal analyzer is an acoustic data set generatedby an acoustic monitoring system, said acoustic data set generated bytransmitting an acoustic signal so that the acoustic signal encounters amaterial of interest, and then detecting the acoustic signal after theacoustic signal has encountered the material of interest. Thus, in afurther embodiment, a system is provided comprising a signal analyzer asdisclosed herein and an acoustic monitoring system discussed in furtherdetail below. Additionally or alternatively, a system may be providedcomprising a signal analyzer as disclosed herein and a non-transitorycomputer readable medium comprising an acoustic data set obtained froman acoustic monitoring system as disclosed herein. In an embodiment, theacoustic data is generated by frequency sweep transmitted and receivedby the acoustic monitoring system. As used herein, the term “frequencysweep” shall refer to a series of acoustic waves transmitted at fixedintervals of frequencies through a medium, such that a first set ofacoustic waves is emitted through the medium at a fixed frequency for afirst fixed duration of time, and subsequent sets of acoustic waves areemitted at fixed frequency intervals for subsequent—preferablyequal—durations.

In some embodiments, the system is adapted for monitoring diffusion of afluid into a porous material. In such an embodiment, a system may beprovided comprising: (a) a signal analyzer as discussed herein; (b) anacoustic monitoring system as discussed herein and/or a non-transitorycomputer readable medium comprising an acoustic data set generated bysaid acoustic monitoring system; and (c) an apparatus for holding aporous material immersed in a volume of a fluid. In an embodiment, saidsystem is for monitoring diffusion of a fixative into a tissue sample.

According to embodiments, the diffusivity constant is determined for thepurpose of characterizing or describing an object, e.g. in the fields ofpharmaceutics, ceramics, metallurgy, materials, manufacturing, earthsciences, soil mechanics, manufacturing and/or engineering. For example,the method may be used for monitoring a staining process of an object,e.g. cloth, plastics, ceramics, tissues or others, for monitoring afixation process, for identifying a material of a particular type, e.g.by comparing the diffusivity constant with known reference diffusivityconstant values of known materials or of materials with a knowncomposition.

According to some further embodiments, the identified diffusivityconstant is used for classifying a biological sample, e.g. a tissuesample. Said classification result may be used, for example, foridentifying the tissue type the sample is derived, for determining ifthe tissue sample is taken from a tumor or from healthy tissue, or forclassifying the tissue samples into different tumor-subtypes. Forexample, from many tumors, it is known that the tumor cells areclustered in close proximity to each other. Samples derived from sometumor types therefore have a different diffusivity constant than samplesof the corresponding healthy tissue. By determining, e.g. in apre-processing step, the diffusivity constants of a samples taken fromdifferent tissue- and/or tumor types, storing the determined diffusivityconstants as reference values and comparing the stored referencediffusivity constants with the diffusivity value obtained according toembodiments of the invention, embodiments of the invention may be usedfor classifying tissue samples.

In an embodiment, an acoustic monitoring system for collecting anacoustic data set is provided, said acoustic monitoring systemcomprising a transmitter and a receiver, wherein said transmitter andreceiver are arranged such that acoustic signals generated by thetransmitter are received by the receiver and transformed into acomputer-readable signal. In an embodiment, the system comprises anultrasonic transmitter and an ultrasonic receiver. As used herein, a“transmitter” is a device capable of converting an electrical signal toacoustic energy, and an “ultrasonic transmitter” is a device capable ofconverting an electrical signal to ultrasonic acoustic energy. As usedherein, a “receiver” is a device capable of converting an acoustic waveto an electrical signal, and an “ultrasonic receiver” is a devicecapable of converting ultrasonic acoustic energy to an electricalsignal.”

Certain materials useful for generating acoustic energy from electricalsignals are also useful for generating electrical signals from acousticenergy. Thus, the transmitter and receiver do not necessarily need to beseparate components, although they can be. The transmitter and receiverare arranged such that the receiver detects acoustic waves generated bythe transmitter after the transmitted waves have encountered a materialof interest. In some embodiments, the receiver is arranged to detectacoustic waves that have been reflected by the material of interest. Inother embodiments, the receiver is arranged to detect acoustic wavesthat have been transmitted through the material of interest.

In an embodiment, the transmitter comprises at least a waveformgenerator operably linked to a transducer, the waveform generator beingconfigured for generating an electrical signal that is communicated tothe transducer, the transducer being configured for converting theelectrical signal to an acoustic signal. In certain embodiments, thewaveform generator is programmable, such that a user may modify certainparameters of the frequency sweep, including for example: startingand/or ending frequency, the step size between frequencies of thefrequency sweep, the number of frequency steps, and/or the duration forwhich each frequency is transmitted. In other embodiments, the waveformgenerator is pre-programmed to generate one or more a pre-determinedfrequency sweep pattern. In other embodiments, the waveform generatormay adapted to transmitted both pre-programmed frequency sweeps andcustomized frequency sweeps. The transmitter may also contain a focusingelement, which allows the acoustic energy generated by the transducer tobe predictably focused and directed to a specific area.

In operation, the transmitter transmits a frequency sweep through themedium, which is then detected by the receiver and transformed into theacoustic data set to be stored in a non-transitory computer readablestorage medium and/or transmitted to the signal analyzer for analysis.Where the acoustic data set includes data representative of a phasedifference between the transmitted acoustic waves and the receivedacoustic waves, the acoustic monitoring system may also include a phasecomparator, which generates an electrical signal that corresponds to thephase difference between transmitted and received acoustic waves. Thus,in certain embodiments, the acoustic monitoring system comprises a phasecomparator communicatively linked to a transmitter and receiver. Wherethe output of the phase comparator is an analog signal, the acousticmonitoring system may also include an analog to digital converter forconverting the analog output of the phase comparator to a digitalsignal. The digital signal may then be recorded, for example, on anon-transitory computer readable medium, or may be communicated directlyto the signal analyzer for analysis.

A signal analyzer is provided containing a processor and a memorycoupled to the processor, the memory to store computer-executableinstructions that, when executed by the processor, cause the processorto calculate a diffusivity constant based at least in part on anacoustic data set generated by an acoustic monitoring system asdiscussed above.

The term “processor” encompasses all kinds of apparatus, devices, andmachines for processing data, including by way of example a programmablemicroprocessor, a computer, a system on a chip, or multiple ones, orcombinations, of the foregoing. The apparatus can include specialpurpose logic circuitry, e.g., an FPGA (field programmable gate array)or an ASIC (application-specific integrated circuit). The apparatus alsocan include, in addition to hardware, code that creates an executionenvironment for the computer program in question, e.g., code thatconstitutes processor firmware, a protocol stack, a database managementsystem, an operating system, a cross-platform runtime environment, avirtual machine, or a combination of one or more of them. The apparatusand execution environment can realize various different computing modelinfrastructures, such as web services, distributed computing and gridcomputing infrastructures.

A computer program (also known as a program, software, softwareapplication, script, or code) can be written in any form of programminglanguage, including compiled or interpreted languages, declarative orprocedural languages, and it can be deployed in any form, including as astand-alone program or as a module, component, subroutine, object, orother unit suitable for use in a computing environment. A computerprogram may, but need not, correspond to a file in a file system. Aprogram can be stored in a portion of a file that holds other programsor data (e.g., one or more scripts stored in a markup languagedocument), in a single file dedicated to the program in question, or inmultiple coordinated files (e.g., files that store one or more modules,subprograms, or portions of code). A computer program can be deployed tobe executed on one computer or on multiple computers that are located atone site or distributed across multiple sites and interconnected by acommunication network.

The processes and logic flows described in this specification can beperformed by one or more programmable processors executing one or morecomputer programs to perform actions by operating on input data andgenerating output. The processes and logic flows can also be performedby, and apparatus can also be implemented as, special purpose logiccircuitry, e.g., an FPGA (field programmable gate array) or an ASIC(application-specific integrated circuit).

Processors suitable for the execution of a computer program include, byway of example, both general and special purpose microprocessors, andany one or more processors of any kind of digital computer. Generally, aprocessor will receive instructions and data from a read-only memory ora random access memory or both. The essential elements of a computer area processor for performing actions in accordance with instructions andone or more memory devices for storing instructions and data. Generally,a computer will also include, or be operatively coupled to receive datafrom or transfer data to, or both, one or more mass storage devices forstoring data, e.g., magnetic, magneto-optical disks, or optical disks.However, a computer need not have such devices. Moreover, a computer canbe embedded in another device, e.g., a mobile telephone, a personaldigital assistant (PDA), a mobile audio or video player, a game console,a Global Positioning System (GPS) receiver, or a portable storage device(e.g., a universal serial bus (USB) flash drive), to name just a few.Devices suitable for storing computer program instructions and datainclude all forms of non-volatile memory, media and memory devices,including by way of example semiconductor memory devices, e.g., EPROM,EEPROM, and flash memory devices; magnetic disks, e.g., internal harddisks or removable disks; magneto-optical disks; and CD-ROM and DVD-ROMdisks. The processor and the memory can be supplemented by, orincorporated in, special purpose logic circuitry.

To provide for interaction with a user, embodiments of the subjectmatter described in this specification can be implemented on a computerhaving a display device, e.g., an LCD (liquid crystal display), LED(light emitting diode) display, or OLED (organic light emitting diode)display, for displaying information to the user and a keyboard and apointing device, e.g., a mouse or a trackball, by which the user canprovide input to the computer. In some implementations, a touch screencan be used to display information and receive input from a user. Otherkinds of devices can be used to provide for interaction with a user aswell; for example, feedback provided to the user can be in any form ofsensory feedback, e.g., visual feedback, auditory feedback, or tactilefeedback; and input from the user can be received in any form, includingacoustic, speech, or tactile input. In addition, a computer can interactwith a user by sending documents to and receiving documents from adevice that is used by the user; for example, by sending web pages to aweb browser on a user's client device in response to requests receivedfrom the web browser.

Embodiments of the subject matter described in this specification can beimplemented in a computing system that includes a back-end component,e.g., as a data server, or that includes a middleware component, e.g.,an application server, or that includes a front-end component, e.g., aclient computer having a graphical user interface or a Web browserthrough which a user can interact with an implementation of the subjectmatter described in this specification, or any combination of one ormore such back-end, middleware, or front-end components. The componentsof the system can be interconnected by any form or medium of digitaldata communication, e.g., a communication network. Examples ofcommunication networks include a local area network (“LAN”) and a widearea network (“WAN”), an inter-network (e.g., the Internet), andpeer-to-peer networks (e.g., ad hoc peer-to-peer networks).

The computing system can include any number of clients and servers. Aclient and server are generally remote from each other and typicallyinteract through a communication network. The relationship of client andserver arises by virtue of computer programs running on the respectivecomputers and having a client-server relationship to each other. In someembodiments, a server transmits data (e.g., an HTML page) to a clientdevice (e.g., for purposes of displaying data to and receiving userinput from a user interacting with the client device). Data generated atthe client device (e.g., a result of the user interaction) can bereceived from the client device at the server.

In operation, the signal analyzer accepts as an input an acoustic dataset recorded from a test material. The acoustic data set isrepresentative of at least a portion of a frequency sweep that isdetected after the frequency sweep encounters a material of interest. Insome embodiments, the portion of the frequency sweep that is detectedconstitutes acoustic waves that are reflected by the material ofinterest. In other embodiments, the portion of the frequency sweep thatis detected constitutes acoustic waves that have passed through thematerial of interest.

FIG. 1 shows an embodiment of a system useful for tissue processing 100for optimized tissue fixation, according to an exemplary embodiment ofthe subject disclosure. System 100 comprises an acoustic monitoringdevice 102 communicatively coupled to a memory 110 for storing aplurality of processing modules or logical instructions that areexecuted by processor 105 coupled to computer 101. Acoustic monitoringdevice 102 may comprise the aforementioned acoustic probes including oneor more transmitters and one or more receivers. The tissue sample may beimmersed in a liquid fixative while the transmitters and receiverscommunicate to detect time of flight (ToF) of acoustic waves. Processingmodules within memory 110 may include logical non-transitorycomputer-readable instructions for enabling processor 105 to performoperations including a tissue analysis module 111 for receivinginformation about the tissue block via user input or electronic inputand for determining tissue characteristics such as an acoustic velocityof the tissue, a TOF modeling module 112 for simulating a spatialdependence of fixative or reagent concentrations for various times andmodel diffusion constants to generate a time-varying (“expected” or“modeled”) TOF signal and outputting a model decay constant by a TOFmeasurement module 113 for determining an actual TOF signal of thetissue, computing a spatial average, and generating an experimentaldecay constant based on tissue characteristics (e.g. cell types, celldensities, cell sizes and effects of sample preparation and/or samplestaining) and input from acoustic monitoring device 102, and acorrelation module 114 for correlating (e.g. comparing) the experimentaland modeled TOF data and determining a true diffusivity constant for thetissue sample based on a minimum of an error function of thecorrelation. These and other operations performed by these modules mayresult in an output of quantitative or graphical results to a useroperations computer 101. Consequently, although not shown in FIG. 1,computer 101 may also include user input and output devices such as akeyboard, mouse, stylus, and a display/touchscreen.

As described above, the modules include logic that is executed byprocessor 105. “Logic”, as used herein and throughout this disclosure,refers to any information having the form of instruction signals and/ordata that may be applied to affect the operation of a processor.Software is one example of such logic. Examples of processors arecomputer processors (processing units), microprocessors, digital signalprocessors, controllers and microcontrollers, etc. Logic may be formedfrom signals stored on a computer-readable medium such as memory 110that, in an exemplary embodiment, may be a random access memory (RAM),read-only memories (ROM), erasable/electrically erasable programmableread-only memories (EPROMS/EEPROMS), flash memories, etc. Logic may alsocomprise digital and/or analog hardware circuits, for example, hardwarecircuits comprising logical AND, OR, XOR, NAND, NOR, and other logicaloperations. Logic may be formed from combinations of software andhardware. On a network, logic may be programmed on a server, or acomplex of servers. A particular logic unit is not limited to a singlelogical location on the network. Moreover, the modules need not beexecuted in any specific order. Each module may call another module whenneeded to be executed.

Acoustic monitoring device 102 may be retrofitted onto a commercialdip-and-dunk tissue processor such as the Lynx II by Electron MicroscopySciences®. A mechanical head designed using Solidworks® software may befit around and seal a standard reagent canister. Once sealed, anexternal vacuum system may initiate to degas the bulk reagent as well asthe contents of the cassette, including the tissue. A cassette holderdesigned for use with either a standard sized histological cassette suchas CellSafe 5 by CellPath® or a biopsy capsule such as CellSafe BiopsyCapsules by CellPath® for smaller tissue samples may be utilized. Eachholder would securely hold the tissue to prevent the sample fromslipping during the experiment. The cassette holder may be attached to avertical translation arm that would slide the cassette holder in onedirection. The mechanical head may be designed with two metal bracketson either side of the tissue cassette, with one bracket housing 5transmitting transducers, and the other bracket housing 5 receivingtransducers that are spatially aligned with their respectivetransmitting transducers. The receiving bracket may also house a pair oftransducers oriented orthogonal to the propagation axis of the othertransducers. After each acquisition the orthogonal sensors may calculatea reference TOF value to detect spatiotemporal variations in the fluidthat has a profound effect on sound velocity. Additionally, at the endof each 2D acquisition, the cassette may be raised up and a secondreference acquisition acquired. These reference TOF values may be usedto compensate for environmentally-induced fluctuations in the formalin.Environmentally-induced fluctuations in the formalin or any otherfixative may be, for example, temperature fluctuations in the containercomprising the porous material, vibrations, and others.

FIGS. 2A and 2B respectively show depictions of ultrasound scan patternsfrom a biopsy capsule and from a standard-sized cassette, according toan exemplary embodiment of the subject disclosure. The measurement andmodeling procedures described in the following for a tissue example maylikewise be applied on other forms of porous material, so the tissuesample is only a non-limiting example for a porous material.

As described herein, the measurements from the acoustic sensors in anacoustic monitoring device may be used to track the change and rate ofchange of a TOF of acoustic signals through the tissue sample. Thisincludes monitoring the tissue sample at different positions over timeto determine diffusion over time or a rate of diffusion.

For example, the “different positions”, also referred to “candidatediffusivity positions” may be a position within or on the surface of thetissue sample. According to some embodiments, the sample may bepositioned at different “sample positions” by a relative movement ofbiopsy capsule and acoustic beam path. The relative movement maycomprise moving the receiver and/or the transducer for “scanning” overthe sample in a stepwise or continuous manner. Alternatively, thecassette may be repositioned by means of a movable cassette holder.

For example, to image all the tissue in the cassette, the cassetteholder may be sequentially raised 1 mm vertically and TOF valuesacquired at each new position, as depicted in FIGS. 2A and 2B. Theprocess may be repeated to cover the entire open aperture of thecassette. Referring to FIG. 2A, when imaging tissue in the biopsycapsule 220, signals are calculated from all 5 transducers pairs,resulting in the scan pattern depicted in FIG. 2A. Alternatively, whenimaging tissue in the standard sized cassette 221 depicted in FIG. 2B,the 2nd and 4th transducer pairs may be turned off and TOF valuesacquired between the 1st, 3rd, and 5th transducer pairs located at therespective centers of the three middle subdivisions of the standardsized cassette 221. Two tissue cores may then be placed in each column,one on the top and one on the bottom, enabling TOF traces from 6 samples(2 rows×3 columns) to simultaneously be obtained and significantlydecreased run to run variation and increased throughput. In thisexemplary embodiment, the full-width-half-maximum of the ultrasound beamis 2.2 mm.

Acoustic sensors in the acoustic monitoring device may include pairs of4 MHz focused transducers such as the TA0040104-10 by CNIRHurricane Tech(Shenzhen) Co., Ltd.® that are spatially aligned, with a tissue samplebeing placed at their common foci. One transducer, designated thetransmitter, may send out an acoustic pulse that traverses the couplingfluid (i.e. formalin) and tissue and is detected by the receivingtransducer.

FIG. 2C shows a timing diagram for an exemplary embodiment of thesubject disclosure. Initially, the transmitting transducer can beprogrammed with a waveform generator such as the AD5930 by AnalogDevices® to transmit a sinusoidal wave for several hundred microseconds.That pulse train may then be detected by the receiving transducer aftertraversing the fluid and tissue. The received ultrasound sinusoid andthe transmitted sinusoid may be compared using, for instance, a digitalphase comparator such as the AD8302 by Analog Devices. The output of thephase comparator yields a valid reading during the region of temporaloverlap between the transmitted and received pulses. The output of thephase comparator is allowed to stabilize before the output is queriedwith an integrated analog to digital converter on the microcontroller,such as the ATmega2560 by Atmel®. The process may then be repeated atmultiple acoustic frequencies across the bandwidth of the transducer tobuild up the phase relationship between the input and output sinusoidsacross a frequency range. This acoustic phase-frequency sweep isdirectly used to calculate the TOF using a post-processing algorithmanalogous to acoustic interferometry and capable of detecting transittimes with subnanosecond accuracy.

Thus according to embodiments of the invention, the “measured TOF”,i.e., the “measured TOF value” obtained for a particular time point anda particular candidate diffusivity point is computed from a measuredphase shift between a transmitted ultrasound signal and thecorresponding, received ultrasound signal, whereby the beam path of theultrasound signal crossed the particular candidate diffusivity point andwhereby the phase shift was measured at the particular time point.

FIG. 3 shows a method for obtaining a diffusivity coefficient for atissue sample, according to an exemplary embodiment of the subjectdisclosure. The operations disclosed with respect to this embodiment maybe performed by any electronic or computer-based system, including thesystem of FIG. 1. These operations may be encoded on a computer-readablemedium such as a memory and executed by a processor, resulting in anoutput that may be presented to a human operator or used in subsequentoperations. Moreover, these operations may be performed in any orderbesides the order disclosed herein, with an understanding of thosehaving ordinary skill in the art, so long as the novel spirit of thesubject disclosure is maintained.

The method may include a calculation of an acoustic velocity for thetissue sample (S330). This operation includes calculating a speed ofsound in the reagent that the tissue sample is immersed in. For example,a distance between ultrasound transducers d_(sensor) i.e., the distancebetween the transmitting transducer and the receiving transducer, may beaccurately measured, and a transit time t_(reagent) between theultrasound transmitter and the ultrasound receiver in pure reagent ismeasured, with the speed of sound in the reagent r_(reagent) beingcalculated using:

$r_{reagent} = \frac{d_{sensor}}{t_{reagent}}$

The tissue thickness may also be obtained via measurement or user input.A variety of suitable techniques are available to obtain tissuethickness, including ultrasound, mechanical, and optical methods.Finally, the acoustic velocity is determined (S330) by obtaining thephase retardation from the undiffused tissue (i.e., a tissue sample towhich the fixation solution has not been applied yet) with respect tothe bulk reagent (e.g. the fixation solution) using:

Δ t = t_(tissue + reagent) − t_(reagent)  and$\frac{1}{r_{tissue}( {t = 0} )} = {\frac{1}{r_{reagent}} + \frac{\Delta \; t}{d_{tissue}}}$

The specific equation is derived based on the known geometry of thetissue sample and, generally, this equation represents the speed ofsound in the undiffused tissue sample (i.e. a tissue sample lacking thereagent, e.g. lacking the fixation solution) at a time t=0. In theexperimental embodiment, for example, the acoustic velocity of a tissuesample may be calculated by first calculating the speed of sound in thereagent based on the distance between the two ultrasound transducers(that are herein also referred to as “sensors”) (d_(sensor)) beingaccurately measured as with a calibrated caliper. In this example, thesensor separation was measured with a caliper and sensor separationd_(sensor)=22.4 mm. Next the transit time (t_(reagent)) required for anacoustic pulse to traverse the reagent (lacking the tissue) between thesensors may be accurately recorded with an applicable program. In theexperimental example, t_(reagent)=16.71 μs for a bulk reagent of 10% NBF(neutral buffered formalin). The sound velocity in the reagent(r_(reagent)) may then be calculated as:

$r_{reagent} = {\frac{d_{sensor}}{t_{reagent}} = {\frac{22.4\mspace{14mu} {mm}}{16.71\mspace{14mu} {µs}} \approx {1.34\mspace{14mu} {mm}\text{/}{µs}}}}$

In this experiment, a sample piece of tonsil was cored with a 6 mmhistological biopsy core punch to ensure accurate and standardizedsample thickness (d_(tissue)=6 mm), and the TOF differential (Δt) wascalculated between the acoustic sensors with the tissue present(t_(tissue+reagent)) and without the tissue present (t_(reagent)):

Δ t = t_(tissue + reagent) − t_(reagent)  Δ t = 16921.3 − 16709.7 = 211.6  ns

The time t_(reagent) is the time required by an ultrasound signal fortraversing the distance from the transmitting transducer to thereceiving transducer, whereby the signal passes a reagent volume but notthe tissue sample. Said traversal time can be measured e.g. by placing abiopsy capsule between the two sensors that has the same diameter as thetissue, e.g. 6 mm, and performing a TOF measurement for a signal thatpasses solely the reagent, not the tissue.

The time t_(tissue) is the time required by an ultrasound signal fortraversing the distance from the transmitting transducer to thereceiving transducer, whereby the signal passes the tissue sample thatdoes not comprise and is not surrounded by the reagent. Said traversaltime can be measured e.g. by placing a biopsy capsule between the twosensors before adding the reagent to the capsule and performing a TOFmeasurement for a signal that passes solely the tissue.

The time differential (or “TOF differential”) Δt caused by the tissue inaddition to the tissue's thickness and the speed of sound in the reagentmay be used to calculate the sound velocity of the undiffused tissue(t_(tissue)(t=0)) with the following equation derived from the knowngeometry (e.g. cylinder-shape, cube-shaped, box-shaped, etc.) of thesample:

$\frac{1}{r_{tissue}( {t = 0} )} = { {\frac{1}{1.34\mspace{14mu} {mm}\text{/}{µs}} + \frac{0.2116\mspace{14mu} {µs}}{6\mspace{14mu} {mm}}}\Rightarrow{r_{tissue}( {t = 0} )}  = {1.28\mspace{14mu} {mm}\text{/}{µs}}}$

Subsequently, a modeling process is executed to model the TOF over avariety of candidate diffusivity constants. The candidate diffusivityconstants comprise a range of constants selected (S331) from known orprior knowledge of tissue properties obtained from the literature. Thecandidate diffusivity constants are not precise, but are simply based ona rough estimate of what the range may be for the particular tissue ormaterial under observation. These estimated candidate diffusivityconstants are provided to the modeling process (steps S332-S335), with aminimal of an error function being determined (S337) to obtain the truediffusivity constant of the tissue. In other words, method tracksdifferences between the experimentally measured TOF diffusion curve anda series of modeled diffusion curves with varying diffusivity constants.

For example, upon selecting one of a plurality of candidate diffusivityconstants, the spatial dependence of the reagent concentration in thetissue sample is simulated (S332), based on a calculation of the reagentconcentration c_(reagent) as a function of time and space, using thesolution to a heat equation for a cylindrical object:

${c_{reagent}( {t,D,x} )} = {c_{\max}( {1 - {2{\sum\limits_{n = 1}^{\infty}\; \frac{e^{{- D}\; \alpha_{n}^{2}{t/R_{0}^{2}}}{J_{0}( {{\alpha_{n}x}R_{o}} )}}{\alpha_{n}{J_{1}( \alpha_{n} )}}}}} )}$

where x is the spatial coordinate in the depth direction of the tissue,R_(o) is the radius of the sample, D is the candidate diffusivityconstant, t is time, J_(o) is a Bessel function of the first kind and0^(th) order, J₁ is a Bessel function of the first kind and 1^(st)order, α_(n) is the location of the n^(th) root of a 0^(th) order Besselfunction, and c_(max) is the maximum concentration of the reagent. Inother words, the summation of the coefficient of each of these Besselfunctions (higher-order differential equations), provides the constantas a function of space, time, and rate, i.e. the diffusivity constant.Although this equation is specific to the cylindrical tissue sampledisclosed in these experimental embodiments, and the equation wouldchange depending on the shape or boundary condition, the solution to theheat equation for any shape may provide the diffusivity constants forthat shape.

This step is repeated for a plurality of time points (S333-S334) toobtain a time-varying TOF (that corresponds to an expected reagentconcentration because the integral of the expected reagent concentrationat a particular time point can be used for computing the speed of sounddifferential) (S335). For example, a determination is made as to whetheror not the diffusion time is complete. This diffusion time may be basedon the hardware or the type of system being used. For each time intervalT, steps S333, S334, and S332 are repeated until the modeling time iscomplete upon which the modeled reagent concentration is converted to atime-varying TOF signal (S335).

In the experimental embodiment, each of the used candidate diffusionconstants D_(candidate) is contained in the following value range:

0.01 ≤ D_(candidate) ≤ 2  µm²/ms

The tissue sample was cored with a cylindrical biopsy core punch andtherefore may be well approximated by a cylinder. The solution to theheat equation above was then used to calculate an expected concentrationof the reagent (c_(reagent)) in the tissue sample and, for the firsttime point in the experiment, i.e. after 104 seconds of diffusion (basedon the time interval between TOF acquisitions used in the systemperforming the disclosed experiment), the solution representing theconcentration of the reagent in the depth direction of the tissue isdepicted in FIG. 5A. For example, a particular system may regularlymeasure a new TOF value for each of a number of different spatiallocations which here are also referred to as “pixels”. Each “pixel” maythus have an update rate of assigning a new TOF value, e.g. every 104seconds.

FIG. 5A shows the simulated concentration gradient of 10% NBF into a 6mm sample of tissue after 104 seconds of passive diffusion as calculatedfrom the heat equation in the experimental embodiment. Moreover, thesesteps were repeated to determine the concentration of the reagentthroughout the tissue repeatedly every 104 s over the course of theexperiment (8.5 hours long in the experimental embodiment), and theresult depicted in FIG. 5B.

FIG. 5B shows a plot of c_(reagent)(t, r) displaying the (“expected”,“modeled”, or “heat equation based”) concentration of the reagent at alllocations in the tissue (horizontal axis) as well as at all times(curves moving upward).

Referring back to FIG. 3, the results of the reagent modeling steps(S332-S334) are used to predict the contribution towards the ultrasoundsignal based on the fact that the ultrasound detection mechanismlinearly builds up phase retardation over the depth of the tissue.

Since the ultrasound detects an integrated signal from all tissue in thedepth direction, i.e. along the propagation axis of the US beam and willthus be sensitive to the integrated amount of fluid exchange in thedepth direction, an “integrated expected” reagent concentrationc_(detected), also referred to as “detected reagent concentration”, maybe calculated. The “detected reagent concentration” is thus not anempirically detected value. Rather, it is a derivative value created byspatially integrating all expected reagent concentrations computed for aparticular time point t and for a particular candidate diffusivityconstant. The spatial integration may cover, for example, the radius ofthe tissue sample.

For example, the detected reagent concentration c_(detected) may becalculated using:

${c_{detected}(t)} = {\frac{2}{R_{o}}{\int_{0}^{R_{o}}{{c_{reagent}( {t,x} )}{dx}}}}$

According to some embodiments, the integrated reagent concentrationc_(detected) is used to calculate the total amount of reagent at aparticular time point. For example, additional volume and/or weightinformation of the sample may be used for calculating absolute reagentamounts. Alternatively, the reagent amount is computed in relativeunits, e.g. as a percentage value indicating e.g. the volume fraction[%] of the sample being already diffused by the reagent.

After simulating (i.e., computing based on the heat equation model) thedetected concentration of the reagent for a given candidate diffusivityconstant and a given time point, that detected concentration may then beconverted into a TOF signal (S335) as a linear combination of undiffusedtissue and reagent, using:

${{TOF}_{tissue}( {t,D} )} = \frac{d_{tissue}}{{r_{tissue}( {t = 0} )} + {\rho \; {c_{detected}(t)}( {{r_{tissue}( {t = 0} )} - r_{reagent}} )}}$

where r_(tissue)(t=0) is the speed of sound of undiffused tissue, and pis the volume porosity of the tissue, representing the fractional volumeof the tissue sample that is capable of fluid exchange with the bulkreagent. This equation therefore models the change in TOF signal fromdiffusion as a linear combination of the two distinct sound velocities(tissue and reagent). As the TOF of the respective sound velocities ofpure tissue on the one hand and pure reagent on the other hand caneasily be determined empirically (e.g. by respective phase-shift basedTOF measurements), the amount of the reagent having already diffusedinto the sample at the particular time point can easily be determined.

According to embodiments, the TOF contribution of the pure tissue sample(being free of the TOF contribution of a bulk fluid such as samplebuffers or the tissue fluid) can be obtained by subtracting the TOFcontribution measured for the tissue sample including and/or beingsurrounded by the bulk fluid from the TOF contribution measured for anultrasound signal having traversed a corresponding inter-transducerdistance filled with said bulk fluid only.

FIGS. 6A and 6B respectively depict a plot of the simulated, “detected”or “integrated” concentration of NBF by the ultrasound over the courseof the experiment (FIG. 6A), and a plot of the simulated (or “expected”)TOF signal for the first candidate diffusivity constant (FIG. 6B, whereD=0.01 μm2/ms). The TOF signals in FIG. 6B are computed as derivativesof the respective integrated concentration of the reagent.

At this point, the method generally correlates (S336) the modeled (or“simulated” or “expected”) TOF with an experimental TOF determined bymeasuring different spatial regions of interest (ROIs), also referred toas “candidate diffusivity points”, within the tissue sample anddetermining a minimum of an error function to obtain a true diffusivityconstant. In this example, each modeled TOF for the specific diffusionconstant selected in the range specified by (S322) is correlated withthe experimental TOF (S336), and determination is made as to whether ornot an error is minimized (S337). If the error is not minimized, thenext diffusion constant is selected (S338) and the modeling process(S332-S335) is repeated for the new diffusion constant. If it isdetermined that the error is minimized (S337) based on correlation(S336), then the true diffusivity constant is determined (S339) and themethod ends.

FIG. 4 shows an alternative method whereby all candidate diffusivityconstants are first used to perform the modeling, based on stepsS446-S447 and the correlation (S448) is performed after all thediffusivity constants are processed. A depiction of the temporallyvarying TOF signal calculated for all potential diffusivity constants isshown in FIG. 7. For example, FIG. 7 depicts simulated TOF traces overthe 8.5 hour experiments for 6 mm tissue samples with diffusivityconstants ranging from 0.01 to 2.0 μm2/ms. In the embodiment of FIG. 4,the error minimization is performed within true diffusivity constantdetermination step S439.

In either case, the experimental TOF must be determined for thecorrelation to take place. The experimental TOF may be determined bymeasuring different spatial regions of interest (ROIs) within thetissue. Each signal has the contribution from background reagentsubtracted out to isolate the contribution from active diffusion intothe tissue. Individual TOF trends are temporally smoothed via filtering.These spatially distinct TOF trends are then spatially-averaged todetermine the average rate of 10% NBF diffusion into the tissue.

FIGS. 8A and 8B respectively depict experimentally calculated TOF trendscollected from a 6 mm piece of human tonsil sample (FIG. 8A) andspatially-averaged TOF signals (FIG. 8B) representing the average rateand amount of fluid exchange of 10% NBF into the tissue.

The average rate of diffusion into the tissue is highly correlated to asingle exponential signal (depicted by the dashed line in FIG. 8B), andderived by:

TOF_(experimental)(t) = Ae^(−t/τ_(experimental)) + offset

where A is the amplitude of the TOF in nanoseconds (i.e., the TOFdifference between the undiffused and fully diffused tissue sample),τ_(experimental) is the sample's decay constant representing the timerequired for the TOF to decay to 37% of its amplitude or equivalently tobe 63% decayed and offset is a vertical offset of the above given decayfunction.

The 63% can be derived by the following calculation: at time t=τ,TOF(τ)=Ae^((−tau/tau))=Ae⁻¹=A/e=A/2.72=0.37*A.

It is hereby assumed that the TOF decreases with an increase in reagentconcentration in the sample, but the method would likewise be applicablefor reagents which increase the measured TOF upon diffusing into thesample. In the 6 mm piece of human tonsil of the experimentalembodiment, τ_(experimental)=2.83 hours. Thus, from a plurality of TOFshaving been experimentally determined for a plurality of consecutivetime points, a decay constant of the tissue sample can be computed, e.g.by plotting the amplitudes of the TOF signal over time, analyzing theplot for identifying the offset and resolving the above solution for thedecay constant.

The error correlation (S336 in FIG. 3, S448 in FIG. 4) is performed todetermine an error of the modeled (“expected”) TOF vs. the experimentalTOF. Having calculated simulated and experimental TOF signals, adifference between the two signals may be calculated to see whether ornot the candidate diffusivity constant minimizes the difference betweenthe two signals (S337).

The error function may be computed in a couple of different ways, forinstance, using one of the following:

${{Error}(D)} = {\frac{1}{N}{\sum\limits_{t = 1}^{N}\; ( {{{TOF}_{simulated}( {t,D} )} - {{TOF}_{experimental}(t)}} )^{2}}}$Error(D) = (τ_(simulated)(D) − τ_(experimental))²

The first error function calculates the point-by-point differencebetween simulated (“modeled”, “expected”) and experimentally measuredTOF signals.

The second error function exclusively compares the rate of diffusionbetween the simulated and modeled TOF signal by calculated thesum-squared differences between each's decay constant. The experimentaldecay constant τ_(experimental) can be obtained experimentally asdescribed above. The “modeled”, “expected” or “simulated” decay constantτ_(simulated) can be derived analogously from the modeled (“expected”)TOFs signal of consecutive time points which also follow a decayfunction.

Based on the output of the error function, a true diffusivity constantmay be determined (S339). The true diffusivity constant is calculated asthe minimum of the error function, for instance:

D _(reconstructed) =arg min(error(D))

This equation enables a determination of the candidate diffusivitycoefficient that produce a TOF signal as close as possible to theexperimental data.

For example, with respect to the method depicted in FIG. 3, the errorfunction may be determined for each candidate diffusivity constant untilthe error is minimized (S337). Alternatively, in the method of FIG. 4,the correlation with experimental TOF may be performed after allcandidate diffusivity constants are processed, upon which thedetermination (S439) of the true diffusivity constant includesdetermining a minimum of the error function. The minimum of the errorfunction is ideally zero, or as closed as possible to zero. Any errorfunction known in the art may be used by those having ordinary skill inthe art, with the goal being to minimize the error between the modeledversus experimental coefficients disclosed herein.

FIGS. 9A and 9B respectively show a plot of the calculated errorfunction between simulated and experimentally measured TOF signals as afunction of candidate diffusivity constant (FIG. 9A, ΔD≈10^(e-5)μm²/ms.), and a zoomed-in view of the error function (FIG. 9B). In theexperimental embodiment, the minimum of the error function wascalculated to be at D=0.1618 μm²/ms. The validity of the reconstructedconstant was tested and used to back-simulate a TOF trend. FIG. 10depicts the TOF trend calculated with this diffusivity constant andplotted alongside the experimental TOF measured with the 6 mm piece ofhuman tonsil. In FIG. 10, the plot shows the experimentally calculatedTOF trend from a 6 mm piece of human tonsil in 10% NBF (dotted line) andthe modeled TOF trend for D_(reconstructed)=0.168 μm²/ms (solid line).In this embodiment, τ_(experimental)=2.830 hrs and τ_(simulated)=2.829hrs.

Furthermore, this same procedure was repeated for several specimens of 6mm human tonsil samples, with successfully reconstructed diffusivityconstants for all samples, as depicted in FIGS. 11A and 11B. FIG. 11Ashows reconstructed diffusivity constants for the 23 samples of 6 mmhuman tonsil. Line 1151 represents the average. FIG. 11B shows a box andwhisker plot displaying the distribution of the reconstructeddiffusivity constants. Line 1152 represents the median value, and thebox 1153 extends from the 25-75 percentiles, with whiskers 1154extending from the 5-95 percentiles. Overall, the algorithm predicted 6mm tonsils samples have an average diffusivity constant of 0.1849 μm2/mswith a relative tight distributed producing a standard deviation of0.0545 μm2/ms.

FIG. 12A shows a system for monitoring the time-of-flight of anultrasound signal according to embodiments of the invention. Anultrasound-based time-of-flight (TOF) monitoring system may comprise oneor more pairs of transducers (e.g. TA0040104-10, CNIRHurricane Tech) forperforming the time-of-flight measurements based on a phase shift of theultrasound signals. In the embodiment depicted in FIG. 12A, the systemcomprises at least one pair of transducers consisting of an ultrasound(“US”) transmitter 902 and an ultrasound receiver 904 which arespatially aligned to each other such that a tissue sample 910 which isplaced in the beam path 914 from the transmitter to the receiver islocated at our close to the common foci of said two transducers 902,904. The tissue sample 910 can be contained, for example, in a samplecontainer 912 (e.g. a standard histological cassette like “CellSafe 5”of CellPath or a biopsy capsule like “CellSafe Biopsy Capsules” ofCellPath) that is filled with a fixation solution. Phase-shift based TOFmeasurements are performed before and after the biopsy capsule 912 isfilled with the fixation solution and while the solution slowly diffusesinto the sample. The one transducer acting as the transmitter sends outan acoustic pulse that traverses the tissue and is detected by the othertransducer acting as the receiver. The total distance between twotransducers constituting a transmitter-receiver transducer pair isreferred to as “L”. The total time the ultrasound signal needs totraverse the distance between the transmitter 902 and the receiver 904may be referred to as time-of-flight of said signal. The transmitter 902may be focused, for example, at 4 MHz and support a frequency sweeprange of 3.7-4.3 MHz.

According to embodiments, the distance L is assumed here to be known, atleast approximately. For example, the distance of the transducers may beaccurately measured (e.g. by optic, ultrasound based or othermeasurement techniques) or may be disclosed by a manufacturer of theacoustic monitoring system.

The transmitting transducer 902 is programmable with a waveformgenerator (e.g. AD5930 from Analog Devices) to transmit a sinusoidalwave (or “sinusoidal signal”) for a defined frequency for a defined timeinterval, e.g. several hundred microseconds. That signal is detected bythe receiving transducer 904 after traversing the fluid and/or tissue.The received ultrasound signal 922 and the emitted (also referred to as“transmitted”) sinusoid signal 920 are compared electronically with adigital phase comparator (e.g. AD8302, Analog Devices).

A “received” “signal” (or wave) as used herein is a signal whoseproperties (phase, amplitude, and/or frequency, etc.) are identified andprovided by a transducer, e.g. receiver 904, that receives said signal.Thus, the signal properties are identified after said signal has passeda sample or any other kind of material.

A “transmitted” or “emitted” “signal” (or wave) as used herein is asignal whose properties (phase, amplitude, and/or frequency, etc.) areidentified by a transducer, e.g. transmitter 902 that emits the signal.Thus, the signal properties are identified before the signal has passeda sample or any other kind of material.

For example, the transmitted signal may be characterized by signalproperties identified by the transmitting transducer, the receivedsignal may be characterized by signal properties measured by thereceiving transducer, whereby the transmitting and the receivingtransducer are operatively coupled to a phase comparator of the acousticmonitoring system.

FIG. 12B depicts the determination of the TOF for the pure reagent fromwhich the speed of the sound wave for the beam path crossing the purereagent without the sample can be inferred. In this embodiment, the oneor more transducer pairs 902, 904 and the sample container 912 can bemoved relative to each other. Preferentially, the system comprises acontainer holder capable of repositioning the container 912 such thatthe US beam traverses a region 914 of the container that solelycomprises the fixation solution but not the tissue.

At a time A, when the tissue is not yet immersed in a fixation solution,the TOF for a sound signal traversing the distance between thetransducers is obtained via a measured phase shift φ_(exp) as describedfor FIG. 12A. In this case, the beam path crosses a sample being free ofthe reagent. As L is known, the measured TOF can be used for computingthe speed of the sound signal for traversing the distance in thepresence of the undiffused sample.

At a time B, when the tissue is immersed in a fixation solution, the TOFfor a sound signal traversing the distance between the transducers isobtained via a measured phase shift φ_(exp). In this case, the beam pathcrosses a sample container comprising only the reagent, not the sample(or crosses the sample container at a position that is free of thesample). As L is known, the measured TOF can be used for computing thespeed of the sound signal for traversing the distance in the presence ofthe reagent (and the sample container) only, i.e., in the absence of thesample in the beam path.

Time A and time B may represent identical time points in case a furthertransducer pair is configured for performing the two measurements inparallel.

In a further aspect, the invention relates to a system 100 comprising anacoustic monitoring device that detects acoustic waves 922 havingtraveled through a porous material 910 and a computing device 101communicatively coupled to the acoustic monitoring device 102. Thecomputing device includes instructions which, when executed, cause thecomputing device to perform operations comprising:

computing a set of experimental TOFs from measured acoustic data of thedetected acoustic waves, each experimental TOF indicating the TOF ofacoustic waves that have traveled through a candidate diffusivity pointof the porous material at a respective one of a plurality of timepoints; the candidate diffusivity point is a location in or at thesurface of the porous material;

setting a range of candidate diffusivity constants for the porousmaterial;

for each of the candidate diffusivity constants, simulating a spatialdependence concentration model of an expected concentration of a reagentwithin the porous material for the plurality of time points and for thecandidate diffusivity point, the expected concentration of the reagentbeing a function of time, space and said candidate diffusivity constant;

using the spatial dependence concentration model for computing a spatialdependence TOF model for the porous material, the TOF model assigning,to the candidate diffusivity point, for each of the plurality of timepoints and for each of the candidate diffusivity constants, arespectively modeled TOF; the expressions “modeled”, “simulated” and“expected” are used herein interchangeably; for example, the “use” mayconsist of converting the spatial dependence concentration model to thespatial dependence TOF model; and

determining an error function for the candidate diffusivity point, theerror being indicative of a distance (that may also be considered as andreferred to as an “error”) between each of the modeled TOFs assigned tosaid candidate diffusivity point from a corresponding experimental TOF,the experimental TOF having been measured by the acoustic monitoringdevice at the same time point as used for modeling its correspondingmodeled TOF;

using the error function for identifying one or more modeled TOFs havingminimum distances to the corresponding experimental TOFs;

outputting a diffusivity constant calculated for the porous materialfrom the candidate diffusivity constants of the one or more identifiedmodeled TOFs.

In a further aspect, the invention relates to a corresponding method.

According to embodiments, the computing the spatial dependence TOF modelcomprises determining each of the modeled TOFs by solving a heatequation for the porous material.

According to embodiments, the computing of a set of experimental TOFs isperformed for two or more candidate diffusivity points of the porousmaterial. The spatial dependence concentration model is a computermodel, e.g. a set of one or more modeling functions, that indicates anexpected concentration of a reagent within the porous material for theplurality of time points and for each of the two or more candidatediffusivity points. The spatial dependence TOF model assigns, to each ofthe two or more candidate diffusivity point, for each of the pluralityof time points and for each of the candidate diffusivity constants, arespectively modeled (or “expected”) TOF.

According to embodiments, the acoustic data comprises: the velocity ofthe sound waves in the porous material prior to diffusion with thereagent; and/or the experimental TOFs of the acoustic waves through theporous material at the plurality of time points during diffusion of thereagent into the porous material; and/or experimental phase shift datafor computing the experimental TOFs from the experimental phase shiftdata; and/or velocity of the sound waves in the reagent being free ofthe porous material; and/or a thickness of the porous material. Forexample, said thickness is determined, according to embodiments, using apulse echo ultrasound.

According to embodiments, the computation of the spatial dependence TOFmodel comprises:

selecting a first one of the candidate diffusivity constants;

calculating an expected reagent concentration creagent at each of theplurality of candidate diffusivity points in the porous material foreach of the plurality of time points in dependence of the selectedcandidate diffusivity constant;

calculating an integrated reagent concentration cdetected for each ofthe plurality of time points and for each of the candidate diffusivityconstants by integrating the expected reagent concentration creagentcalculated for said time point and said candidate diffusivity constantover a radius of the porous material;

converting the integrated reagent concentration to a modeled TOF of thespatial dependence TOF model by computing a linear combination of thespeed of the sound waves in the porous material prior to diffusion withthe reagent and the speed of the sound waves in the reagent being freeof the porous material; and

selecting a next one of the candidate diffusivity constants andrepeating this step and the three previous steps for the next selectedcandidate diffusivity constant until a termination criterion is reached.

In summary, determination of diffusivity constants for any samplematerial may be provided by calculating the speed of sound in a reagentat a given temperature, pressure, etc., determining the sample'sthickness with standard pulse echo ultrasound, determining the absolutesound velocity in the undiffused sample via phase retardation ofultrasound, followed by generating the modeled TOF trend from thecandidate diffusivity constant first simulating the spatial dependenceof the reagent diffusion into the sample, summing the total reagentconcentration detected by the ultrasound beam, converting the detectedreagent concentration to the TOF differential, and repeating these stepsfor multiple diffusion times. Then, the modeled TOF trend is determinedby repeating the spatial dependence simulation for a plurality ofcandidate diffusivity constants (as provided by the known literature)and calculating an error between the experimental and simulated TOFdifferentials at all times and for all diffusivity constants, resultingin an error function between the experimental and modeled TOF as afunction of diffusivity constant. Calculating the true diffusivityconstant as the minimum of the error function results in an output.

Moreover, the subject disclosure applies to both biological andnon-biological context, providing an ability to reconstruct thediffusivity constant of any substance based on the acoustic TOF curve.The disclosed methods are more sensitive and accurate when compared toprior art methods. Although the disclosed operations provide fitting theTOF curve to a single exponential function comprising a summation ofBessel functions, a double exponential or quadratic function may be moreappropriate, depending on the context. Therefore, the equation itselfmay change, while the novel features disclosed herein may maintain theirinventive spirit and scope when read by a person having ordinary skillin the art.

III. Exemplary Applications of the Present Systems and Methods

Diffusivity constant calculations are known to be useful for manyapplications, including compositional analysis. The present systems andmethods are contemplated to be used in any system that utilizes adiffusivity constant measurement. In one specific embodiment, thepresent systems and methods are applied to the field of monitoringdiffusion of fluids into porous materials.

In one particular embodiment, the porous material is a tissue sample. Inmany common tissue analysis methods, the tissue sample is diffused witha fluid solution. For example, Hine (Stain Technol. 1981 March;56(2):119-23) discloses a method of staining whole tissue blocks byimmersing a tissue sample in a hematoxylin solution and eosin solutionafter fixation and prior to embedding and sectioning. Additionally,fixation is frequently performed by immersing an unfixed tissue sampleinto a volume of fixative solution, and the fixative solution is allowedto diffuse into the tissue sample. As demonstrated by Chafin et al.,(PLoS ONE 8(1): e54138. doi:10.1371/journal.pone. 0054138 (2013)), afailure to ensure that a fixative has sufficiently diffused into thetissue can compromise the integrity of the tissue sample. Thus, in oneembodiment, the present systems and methods are applied to determine asufficient time of diffusion of a fixative into a tissue sample. In sucha method, the user selects a minimum fixative concentration to beachieved at a particular point in the tissue sample (such as the centerof the thickness of the tissue sample). Knowing at least the tissuethickness, tissue geometry, and the calculated true diffusivityconstant, a person of ordinary skill in the art could apply well-known“diffusion” or “diffusivity” algorithms to determine a minimum time toreach the minimum fixative concentration at the center of the tissuesample. The fixative will thus be allowed to diffuse into the tissuesample for at least said minimum time.

In an embodiment, the present systems and methods are used to run atwo-temperature immersion fixation method on a tissue sample. As usedherein, a “two-temperature fixation method” is a fixation method inwhich tissue is first immersed in cold fixative solution for a firstperiod of time, followed by heating the tissue for the second period oftime. The cold step permits the fixative solution to diffuse throughoutthe tissue without substantially causing cross-linking. Then, once thetissue has adequately diffused throughout the tissue, the heating stepleads to cross-linking by the fixative. The combination of a colddiffusion followed by a heating step leads to a tissue sample that ismore completely fixed than by using standard methods. Thus, in anembodiment, a tissue sample is fixed by: (1) immersing an unfixed tissuesample in a cold fixative solution and monitoring diffusion of thefixative into the tissue sample by monitoring TOF in the tissue sampleusing the systems and methods as disclosed herein (diffusion step); and(2) allowing the temperature of the tissue sample to raise after athreshold TOF has been measured (fixation step). In exemplaryembodiments, the diffusion step is performed in a fixative solution thatis below 20° C., below 15° C., below 12° C., below 10° C., in the rangeof 0° C. to 10° C., in the range of 0° C. to 12° C., in the range of 0°C. to 15° C., in the range of 2° C. to 10° C., in the range of 2° C. to12° C., in the range of 2° C. to 15° C., in the range of 5° C. to 10°C., in the range of 5° C. to 12° C., in the range of 5° C. to 15° C. Inexemplary embodiments, the environment surrounding the tissue sample isallowed to rise within the range of 20° C. to 55° C. during the fixationstep. In certain embodiments, the fixative is an aldehyde-basedcross-linking fixative, such as glutaraldehyde- and/or formalin-basedsolutions. Examples of aldehydes frequently used for immersion fixationinclude:

formaldehyde (standard working concentration of 5-10% formalin for mosttissues, although concentrations as high as 20% formalin have been usedfor certain tissues);

glyoxal (standard working concentration 17 to 86 mM);

glutaraldehyde (standard working concentration of 200 mM).

Aldehydes are often used in combination with one another. Standardaldehyde combinations include 10% formalin+1% (w/v) Glutaraldehyde.Atypical aldehydes have been used in certain specialized fixationapplications, including: fumaraldehyde, 12.5% hydroxyadipaldehyde (pH7.5), 10% crotonaldehyde (pH 7.4), 5% pyruvic aldehyde (pH 5.5), 10%acetaldehyde (pH 7.5), 10% acrolein (pH 7.6), and 5% methacrolein (pH7.6). Other specific examples of aldehyde-based fixative solutions usedfor immunohistochemistry are set forth in Table 1:

TABLE 1 Solution Standard Composition Neutral Buffered 5-20% formalin +phosphate buffer (pH~6.8) Formalin Formal Calcium 10% formalin + 10 g/Lcalcium chloride Formal Saline 10% formalin + 9 g/L sodium chloride ZincFormalin 10% formalin + 1 g/L zinc sulphate Helly's Fixative 50 mL 100%formalin + 1 L aqueous solution containing 25 g/L potassium dichromate +10 g/L sodium sulfate + 50 g/L mercuric chloride B-5 Fixative 2 mL 100%formalin + 20 mL aqueous solution containing 6 g/L mercuric chloride +12.5 g/L sodium acetate (anhydrous) Hollande's 100 mL 100% formalin + 15mL Acetic acid + Solution 1 L aqueous solution comprising 25 g copperacetate and 40 g picric acid Bouin's Solution 250 mL 100% formalin + 750mL saturated aqueous picric acid + 50 mL glacial acetic acid

In certain embodiments, the fixative solution is selected from Table 1.In some embodiments, the aldehyde concentration used is higher than theabove-mentioned standard concentrations. For example, ahigh-concentration aldehyde-based fixative solution can be used havingan aldehyde concentration that is at least 1.25-times higher than thestandard concentration used to fix a selected tissue forimmunohistochemistry with a substantially similar composition. In someexamples, the high-concentration aldehyde-based fixative solution isselected from: greater than 20% formalin, about 25% formalin or greater,about 27.5% formalin or greater, about 30% formalin or greater, fromabout 25% to about 50% formalin, from about 27.5% to about 50% formalin,from about 30% to about 50% formalin, from about 25% to about 40%formalin, from about 27.5% to about 40% formalin, and from about 30% toabout 40% formalin. As used in this context, the term “about” shallencompass concentrations that do not result in a statisticallysignificant difference in diffusion at 4° C. as measured by Bauer etal., Dynamic Subnanosecond Time-of-Flight Detection for Ultra-preciseDiffusion Monitoring and Optimization of Biomarker Preservation,Proceedings of SPIE, Vol. 9040, 90400B-1 (2014 Mar. 20).

Two-temperature fixation processes are especially useful for methods ofdetecting certain labile biomarkers in tissue samples, including, forexample, phosphorylated proteins, DNA, and RNA molecules (such as miRNAand mRNA). See PCT/EP2012/052800 (incorporated herein by reference).Thus, in certain embodiments, the fixed tissue samples obtained usingthese methods can be analyzed for the presence of such labile markers.Thus in an embodiment, a method of detecting a labile marker is a sampleis provided, said method comprising fixing the tissue according to atwo-temperature fixation as disclosed herein and contacting the fixedtissue sample with an analyte binding entity capable of bindingspecifically to the labile marker. Examples of analyte-binding entitiesinclude: antibodies and antibody fragments (including single chainantibodies), which bind to target antigens; t-cell receptors (includingsingle chain receptors), which bind to MHC:antigen complexes; MHC:peptide multimers (which bind to specific T-cell receptors); aptamers,which bind to specific nucleic acid or peptide targets; zinc fingers,which bind to specific nucleic acids, peptides, and other molecules;receptor complexes (including single chain receptors and chimericreceptors), which bind to receptor ligands; receptor ligands, which bindto receptor complexes; and nucleic acid probes, which hybridize tospecific nucleic acids. For example, an immunohistochemical method ofdetecting a phosphorylated protein in a tissue sample is provided, themethod comprising contacting the fixed tissue obtained according to theforegoing two-temperature fixation method with an antibody specific forthe phosphorylated protein and detecting binding of the antibody to thephosphorylated protein. In other embodiments, an in situ hybridizationmethod of detecting a nucleic acid molecule is provided, said methodcomprising contacting the fixed tissue obtained according to theforegoing two-temperature fixation method with a nucleic acid probespecific for the nucleic acid of interest and detecting binding of theprobe to the nucleic acid of interest.

IV. Other Embodiments of the Disclosed System and Method Embodiment 1

A system (100) comprising: an acoustic monitoring device that detectsacoustic waves (922) having traveled through a porous material (910);and a computing device (101) communicatively coupled to the acousticmonitoring device (102), the computing device including instructionswhich, when executed, cause the computing device to perform operationscomprising: computing a set of experimental TOFs from measured acousticdata of the detected acoustic waves, each experimental TOF indicatingthe TOF of acoustic waves that have traveled through a candidatediffusivity point of the porous material at a respective one of aplurality of time points; setting a range of candidate diffusivityconstants for the porous material; for each of the candidate diffusivityconstants, simulating a spatial dependence concentration model of anexpected concentration of a reagent within the porous material for theplurality of time points and for the candidate diffusivity point, theexpected concentration of the reagent being a function of time, spaceand said candidate diffusivity constant; using the spatial dependenceconcentration model for computing a spatial dependence TOF model for theporous material, the TOF model assigning, to the candidate diffusivitypoint, for each of the plurality of time points and for each of thecandidate diffusivity constants, a respectively modeled TOF; anddetermining an error function for the candidate diffusivity point, theerror being indicative of a distance between each of the modeled TOFsassigned to said candidate diffusivity point from a correspondingexperimental TOF, the experimental TOF having been measured by theacoustic monitoring device at the same time point as used for modelingits corresponding modeled TOF; using the error function for identifyingone or more modeled TOFs having minimum distances to the correspondingexperimental TOFs; and, outputting a diffusivity constant calculated forthe porous material from the candidate diffusivity constants of the oneor more identified modeled TOFs.

Embodiment 2

A method for determining a diffusivity constant of a porous material(910) comprising: computing a set of experimental TOFs from measuredacoustic data of acoustic waves (922), the acoustic waves having beendetected by an acoustic monitoring device (102) and having traveledthrough the porous material (910), each experimental TOF indicating theTOF of acoustic waves that have traveled through a candidate diffusivitypoint of the porous material at a respective one of a plurality of timepoints; setting a range of candidate diffusivity constants for theporous material; for each of the candidate diffusivity constants,simulating a spatial dependence concentration model of an expectedconcentration of a reagent within the porous material for the pluralityof time points and for the candidate diffusivity point, the expectedconcentration of the reagent being a function of time, space and saidcandidate diffusivity constant; using the spatial dependenceconcentration model for computing a spatial dependence TOF model for theporous material, the TOF model assigning, to the candidate diffusivitypoint, for each of the plurality of time points and for each of thecandidate diffusivity constants, a respectively modeled TOF; and,determining an error function for the candidate diffusivity point, theerror being indicative of a distance between each of the modeled TOFsassigned to said candidate diffusivity point from a correspondingexperimental TOF, the experimental TOF having been measured by theacoustic monitoring device at the same time point as used for modelingits corresponding modeled TOF; using the error function for identifyingone or more modeled TOFs having minimum distances to the correspondingexperimental TOFs; outputting a diffusivity constant calculated for theporous material from the candidate diffusivity constants of the one ormore identified modeled TOFs.

Embodiment 3

The method of embodiment 2, wherein computing the spatial dependence TOFmodel comprises determining each of the modeled TOFs by solving a heatequation for the porous material.

Embodiment 4

The method of any one of embodiments 2-3, the computing of a set ofexperimental TOFs being performed for two or more candidate diffusivitypoints of the porous material, the spatial dependence concentrationmodel indicating an expected concentration of a reagent within theporous material for the plurality of time points and for each of the twoor more candidate diffusivity points, the spatial dependence TOF modelassigning, to each of the two or more candidate diffusivity point, foreach of the plurality of time points and for each of the candidatediffusivity constants, a respectively modeled TOF.

Embodiment 5

The method of any one of embodiments 2-4, the acoustic data comprising:velocity of the sound waves in the porous material prior to diffusionwith the reagent; and/or the experimental TOFs of the acoustic wavesthrough the porous material at the plurality of time points duringdiffusion of the reagent into the porous material; and/or experimentalphase shift data for computing the experimental TOFs from theexperimental phase shift data; velocity of the sound waves in thereagent being free of the porous material; and/or a thickness of theporous material.

Embodiment 6

The method of any one of embodiments 2-5, the computation of the spatialdependence TOF model comprising: selecting a first one of the candidatediffusivity constants; calculating an expected reagent concentration(creagent) at each of the plurality of candidate diffusivity points inthe porous material for each of the plurality of time points independence of the selected candidate diffusivity constant; calculatingan integrated reagent concentration (cdetected) for each of theplurality of time points and for each of the candidate diffusivityconstants by integrating the expected reagent concentration (creagent)calculated for said time point and said candidate diffusivity constantover a radius of the porous material; converting the integrated reagentconcentration to a respective modeled TOF of the spatial dependence TOFmodel by computing a linear combination of the speed of the sound wavesin the porous material prior to diffusion with the reagent and the speedof the sound waves in the reagent being free of the porous material; andselecting a next one of the candidate diffusivity constants andrepeating this step and the three previous steps for the next selectedcandidate diffusivity constant until a termination criterion is reached.

Embodiment 7

The method of embodiment 6, wherein the speed of sound waves in thereagent is calculated by transmitting an ultrasonic wave between anultrasonic transmitter and an ultrasonic receiver through the fluid,calculating the TOF between the transmitter and receiver, andcalculating the speed of the sound wave of the reagent according to thefollowing formula:

$r_{fluid} = \frac{d}{t}$

wherein r_(fluid) is the speed of sound in the reagent, d is thedistance between the transmitter and receiver, and t is the TOF betweenthe transmitter and receiver.

Embodiment 8

The method of embodiment 6 or 7, wherein the speed of the sound wafes inthe undiffused porous material (r_(orig)) is determined according to thefollowing formula:

$\frac{1}{r_{orig}} = {\frac{1}{r_{fluid}} + \frac{\Delta \; t}{d_{mat}}}$

wherein Δt is the difference in TOF between waves passing through thereagent and the porous material and waves passing through the reagentonly, and d_(mat) is the thickness of the porous material.

Embodiment 9

The method of any of any one of embodiments 2-8, wherein the spatialdependence concentration model is configured to calculate the expectedconcentration of the reagent at the candidate diffusivity point by usinga heat equation, the heat equation being descriptive of the distributionof heat in a given region of an object having the same 3D shape as theporous material over time.

Embodiment 10

The method of embodiment 9, wherein the porous material is cylindricaland the heat equation is specified by the following formula:

${c_{fluid}( {t,D,x} )} = {c_{\max}( {1 - {2{\sum\limits_{n = 1}^{\infty}\; \frac{e^{{- D}\; \alpha_{n}^{2}{t/R_{0}^{2}}}{J_{0}( {\alpha_{n}x\text{/}R_{o}} )}}{\alpha_{n}{J_{1}( \alpha_{n} )}}}}} )}$

wherein c_(fluid) is the expected concentration of the reagent, t is thediffusion time at the selected time point, D is the candidatediffusivity constant, x is the spatial coordinate of the candidatediffusivity point in the depth direction of the porous material, R_(o)is the radius of the porous material, J_(o) is a Bessel function of thefirst kind and 0^(th) order, J₁ is a Bessel function of the first kindand 1^(st) order, α_(n) is the location of the n^(th) root of a 0^(th)order Bessel function, and c_(max) is the maximum concentration of thereagent.

Embodiment 11

The method of any one of embodiments 2-10, the using of the spatialdependence concentration model for computing the spatial dependence TOFmodel comprising: using a heat equation of an object having the same 3Dshape as the porous material for computing, for each unique combinationof a time point, a candidate diffusivity constant and a candidatediffusivity point, a respective expected reagent concentration(c_(fluid)); computing, from all expected reagent concentration(c_(fluid)) computed for a particular time point, an integrated expectedreagent concentration (c_(determined)) by integrating the expectedreagent concentrations (c_(fluid)) of said time point spatially over theradius of the porous material; converting each of the integratedexpected reagent concentrations (c_(determined)) into a respective oneof the modeled TOFs of the spatial dependence TOF model.

Embodiment 12

The method of embodiment 11, the computing of the integrated expectedreagent concentration (c_(determined)) being performed according to thefollowing formula:

${{c_{detected}(t)} = {\frac{2}{R_{o}}{\int_{0}^{R_{o}}{{c_{fluid}( {t,x} )}{dx}}}}}\ $

wherein c_(fluid) is the expected concentration of the reagent, t is thediffusion time at the selected time point, c_(detected) is theintegrated expected reagent concentration, x is the spatial coordinateof the candidate diffusivity point in the depth direction of the porousmaterial, and R_(o) is the radius of the porous material.

Embodiment 13

The method of embodiment 11 or 12, wherein the converting of each of theintegrated expected reagent concentrations (c_(determined)) into arespective one of the modeled TOFs of the spatial dependence TOF modelis computed according to the following formula:

${{TOF}_{simulated}( {t,D} )} = \frac{d_{mat}}{{r_{orig}( {t = 0} )} + {\rho \; {c_{detected}(t)}( {{r_{orig}( {t = 0} )} - r_{fluid}} )}}$

wherein TOF is one of the modeled TOF values of the spatial dependencyTOF model resulting from the conversion, r_(orig) is the speed of thesound wave in the porous material being free of the reagent, r_(fluid)is the speed of the sound wave in the reagent being free of the porousmaterial, c_(determined) is the integrated expected reagentconcentration, D is the candidate diffusivity constant, t is thediffusion time at the selected time point, and p is the volume porosityof the porous material and wherein d_(mat) is the thickness of theporous material.

Embodiment 14

The method of any one of embodiments 2-13, wherein the error function iscalculated according to the following formula:

${{Error}(D)} = {\frac{1}{N}{\sum\limits_{t = 1}^{N}\; {( {{{TOF}_{simulated}( {t,D} )} - {{TOF}_{experimental}(t)}} )^{2}.}}}$

Embodiment 15

The method of any one of embodiments 2-14, further comprising:

analyzing a plurality of the modeled TOFs of the spatial dependence TOFmodel relating to a particular candidate diffusivity point and to aparticular candidate diffusivity constants and having been modeled fordifferent time points, the analysis being performed for identifying anexpected decay constant (τ_(simulated)), the expected decay constantindicating a time span after which the modeled TOFs have decayed by apredefined percentage; analyzing a plurality of the measured TOFs of thespatial dependence TOF model relating to the particular candidatediffusivity point and to the particular candidate diffusivity constantsand having been measured at the different time points, the analysisbeing performed for identifying an experimental decay constant(τ_(experimental)), the experimental decay constant indicating a timespan after which the experimental TOFs have decayed by a predefinedpercentage; wherein the error function is calculated according to thefollowing formula:

Error(D) = (τ_(simulated)(D) − τ_(experimental))²

wherein D is the candidate diffusivity constant.

Embodiment 16

The method according to any one of embodiments 2-15 being performed by aprocessor of a computer system communicatively coupled to the acousticmonitoring device.

Embodiment 17

The method according to any one of embodiments 2-16 comprising:

acquiring a reference time, the reference time indicating a time ofsufficient diffusion of the porous material with the reagent;calculating a sufficient diffusion time from the output diffusivityconstant; and leaving the tissue sample immersed in the fixative for atleast the calculated sufficient diffusion time.

Embodiment 18

The method of any one of embodiments 2-17, the reagent being a liquid,the plurality of time points respectively indicating the time havinglapsed since the porous material was immersed into a volume of theliquid.

Embodiment 19

The method of any one of embodiments 2-18, the reagent being a fixationsolution and/or the porous material being a tissue sample.

Embodiment 20

The method of any one of embodiments 2-19, further comprising: immersingthe porous material in the reagent; keeping the immersed porous materialat a temperature from 0° C. to 15° C. while the acoustic waves aredetected; for each of the plurality of time points, comparing theexperimental TOF with a reference TOF, wherein the reference TOFindicates that the tissue sample is sufficiently diffused with thereagent; in case the experimental TOF reaches the threshold, allowingthe temperature of the tissue sample and the reagent to rise to theambient temperature or triggering the heating of the temperature of thetissue sample and the reagent to a temperature of more than 20° C.

Embodiment 21

The method of any one of embodiments 2-19, further comprising:

fixing the tissue sample to obtain a fixed tissue sample; contacting thefixed tissue sample with a specific binding entity capable of binding tothe labile biomarker; and

detecting binding of the specific binding entity.

Embodiment 22

A tangible non-transitory computer-readable medium to storecomputer-readable code that is executed by a processor to perform themethod according to any one of embodiments 2-16.

Embodiment 23

A method for determining a true diffusivity constant for a sampleimmersed within a reagent, the method comprising: simulating a spatialdependence of a diffusion into the sample over a plurality of timepoints and for each of a plurality of candidate diffusivity constants togenerate a model time-of-flight; and comparing the model time-of-flightwith an experimental time-of-flight to obtain an error function;

wherein a minimum of the error function yields the true diffusivityconstant.

Embodiment 24

The method of embodiment 23, wherein the plurality of candidatediffusivity constants comprises a range of candidate diffusivityconstants provided by an external source.

Embodiment 25

The method of any one of embodiments 23-24, further comprisingdetermining an absolute acoustic velocity for the sample.

Embodiment 26

The method of embodiment 25, wherein determining the acoustic velocitycomprises calculating the speed of sound in the reagent, and determiningthe thickness of the sample.

Embodiment 27

The method of any one of embodiments 23-26, wherein simulating thespatial dependence further comprises determining a model concentrationof the reagent through the sample over the plurality of time points.

Embodiment 28

The method of embodiment 27, wherein simulating the spatial dependencefurther comprises determining a concentration of the reagent as afunction of time and space using the solution to a heat equation for thesample.

Embodiment 29

The method of embodiment 28, wherein the solution to the heat equationfor the sample is based on a geometry of the sample.

Embodiment 30

The method of any one of embodiments 27-29, wherein simulating thespatial dependence further comprises converting the model concentrationinto a time-of-flight.

Embodiment 31

The method of embodiment 30, wherein the model time-of-flight isobtained by determining a time-of-flights for each of the plurality ofcandidate diffusivity constants.

Embodiment 32

The method of any one of embodiments 23-31, wherein the error functionis based on a point-by-point difference between the model time-of-flightand the experimental time-of-flight.

Embodiment 33

The method of any one of embodiments 23-32, wherein the error functionis based on a rate of diffusion between the model time-of-flight and theexperimental time-of-flight.

Embodiment 34

The method of any one of embodiments 23-33, further comprisingdetermining an error between an experimental and simulatedtime-of-flight for each candidate diffusivity constant.

Embodiment 35

The method of embodiment 34, wherein the error function is based on theerror.

Embodiment 36

A system comprising: an acoustic monitoring device that detects acousticwaves that have traveled through a tissue sample; and a computing devicecommunicatively coupled to the acoustic monitoring device, the computingdevice is configured to evaluate a speed of the acoustic waves based ona time of flight and including instructions, when executed, for causingthe processing system to perform operations comprising: setting a rangeof candidate diffusivity constants for the tissue sample; simulating aspatial dependence of a reagent within the tissue sample for a pluralityof time points and for a first of the range of candidate diffusivitypoints;

determining a modeled time-of-flight based on the spatial dependence;repeating the spatial dependence simulation for each of the plurality ofdiffusivity constants; and

determining an error between the modeled-time-of-flight for theplurality of diffusivity constants versus an experimental time-of-flightfor the tissue sample;

wherein a minimum of an error function based on the error yields a truediffusivity constant for the tissue sample.

Embodiment 37

The system of embodiment 36, wherein the operations further comprisesolving a heat equation for the tissue sample to determine the modeledtime-of-flight.

Embodiment 38

The system of embodiment 36 or 37, wherein the error is determined foreach candidate diffusivity constant.

Embodiment 39

The system of embodiment 37, wherein the error function is determinedfrom the error for each diffusivity constant as a function of thediffusivity constant.

Embodiment 40

A tangible non-transitory computer-readable medium to storecomputer-readable code that is executed by a processor to performoperations comprising: comparing a simulated time-of-flight for a samplematerial with an experimental time-of-flight for the sample material;and obtaining a diffusivity constant for the sample material based on aminimum of an error function between the simulated time-of-flight andthe acoustic time-of-flight.

Embodiment 41

A method of determining a diffusivity constant of a fluid diffusing intoa porous material, said method comprising: immersing a sample of theporous material into a volume of the fluid; collecting a set of acousticdata for the sample of the porous material immersed in the volume of thefluid with an acoustic monitoring system and transmitting said acousticdata set to a signal analyzer, said acoustic data set comprising: (b1)absolute sound velocity of ultrasonic waves in the porous material priorto diffusion with fluid; (b2) TOF of ultrasonic waves through the porousmaterial at least at one time point during diffusion of fluid into theporous material (TOF_(experimental)); (b3) absolute sound velocity ofultrasonic waves in the fluid; and (b4) a thickness of the porousmaterial; (c) calculating a diffusivity constant for diffusion of thefluid into the porous material on a signal analyzer by: (c1) modeling aTOF trend for each of a plurality of candidate diffusivity constants by:(c1a) selecting a first candidate diffusivity constant; (c1b) selectinga plurality of diffusion times corresponding to the time points of (b2);(c1c) calculating a concentration of the fluid at each of a plurality ofdepths through thickness (b4) of the porous sample as a function of timeand space; (c1d) calculating a total amount of diffused reagent at eachtime point (c_(detected)) (c1e) calculating an expected TOF differentialresulting from the concentration determined in (c1d) as a linearcombination of (b1) and (b3); and (c1f) repeating (c1a)-(c1e) for aplurality of candidate diffusivity constants; (c2) calculating an errorfunction between the TOF of (b2) and each of the TOF differentialscalculated from (c1) as a function of diffusivity constant, wherein thetrue diffusivity constant is a minimum of the error function.

Embodiment 42

The method of embodiment 41, wherein the speed of sound in the fluid iscalculated by transmitting an ultrasonic wave between an ultrasonictransmitter and an ultrasonic receiver through the fluid, calculatingthe time of flight between the transmitter and receiver, and calculatingthe speed of sound according to the following formula:

$r_{fluid} = \frac{d}{t}$

wherein r_(fluid) is the speed of sound in the fluid, d is the distancebetween the transmitter and receiver, and t is the time of flight (TOF)between the transmitter and receiver.

Embodiment 43

The method of embodiment 42, wherein the speed of sound in theundiffused porous material (r_(orig)) is determined according to thefollowing formula:

$\frac{1}{r_{orig}} = {\frac{1}{r_{fluid}} + \frac{\Delta \; t}{d_{mat}}}$

wherein Δt is the difference in TOF between waves passing through thefluid and the porous material and waves passing through the fluid only,and d_(mat) is the thickness of the porous material.

Embodiment 44

The method of any of embodiments 41-43, wherein the thickness of theporous material is determined using a pulse echo ultrasound.

Embodiment 45

The method of any of embodiments 41-44, wherein the porous material iscylindrical and the concentration of the fluid at each of the pluralityof depths through thickness (b4) of the porous sample is calculatedaccording to the following formula:

${c_{fluid}( {t,D,x} )} = {c_{\max}( {1 - {2{\sum\limits_{n = 1}^{\infty}\; \frac{e^{{- D}\; \alpha_{n}^{2}{t/R_{0}^{2}}}{J_{0}( {\alpha_{n}x\text{/}R_{o}} )}}{\alpha_{n}{J_{1}( \alpha_{n} )}}}}} )}$

wherein c_(fluid) is the concentration, t is the diffusion time at theselected time point, D is the candidate diffusivity constant, x is thespatial coordinate in the depth direction of the tissue, R_(o) is theradius of the sample, J_(o) is a Bessel function of the first kind and0^(th) order, J₁ is a Bessel function of the first kind and Pt order,α_(n) is the location of the n^(th) root of a 0^(th) order Besselfunction, and c_(max) is the maximum concentration of the reagent.

Embodiment 46

The method of embodiment 45, wherein the total amount of diffusedreagent (c_(detected)) is calculated according to the following formula:

${{c_{detected}(t)} = {\frac{2}{R_{o}}{\int_{0}^{R_{o}}{{c_{fluid}( {t,x} )}{dx}}}}}\ $

Embodiment 47

The method of embodiment 46, wherein the expected TOF differential iscalculated according to the following formula:

${{TOF}_{simulated}( {t,D} )} = \frac{d_{mat}}{{r_{orig}( {t = 0} )} + {\rho \; {c_{detected}(t)}( {{r_{orig}( {t = 0} )} - r_{fluid}} )}}$

wherein d_(mat) is the thickness of the material and p is porosity ofthe material.

Embodiment 48

The method of embodiment 47, wherein the error function is calculatedaccording to the following formula:

${{Error}(D)} = {\frac{1}{N}{\sum\limits_{t = 1}^{N}\; {( {{{TOF}_{simulated}( {t,D} )} - {{TOF}_{experimental}(t)}} )^{2}.}}}$

Embodiment 49

The method of any of embodiments 41-48, wherein said porous material isa tissue sample and the fluid is a fixative solution.

Embodiment 50

A method of fixing a tissue sample, said method comprising calculating adiffusivity constant of a tissue sample immersed in a fixative solutionaccording to a method of embodiment 49, calculating a sufficientdiffusion time based upon the calculated diffusivity constant, andleaving the tissue sample immersed in the fixative for at least thecalculated sufficient diffusion time.

Embodiment 51

A method of fixing a tissue sample, said method comprising: obtaining atissue sample sufficiently diffused with a cross-linking fixativesolution by: (a1) immersing an unfixed tissue sample freshly obtainedfrom a subject into a volume of the cross-linking fixative solution,wherein the cross-linking fixative is at a temperature from 0° C. to 15°C.; (a2) calculating a diffusivity constant according to a method ofembodiment 28; and (a3)determining a sufficient diffusion time based onthe calculated diffusivity constant; (b) after the tissue sample hasbeen immersed in the cross-linking fixative solution for the sufficientdiffusion time, raising the temperature of the tissue sample to atemperature in the range of room temperature to 50° C., and holding thetissue sample in said range of temperatures for a period of timesufficient to allow fixation of the tissue sample.

Embodiment 52

A method of detecting a labile biomarker in a tissue sample, said methodcomprising: fixing the tissue sample according to the method ofembodiment 30 to obtain a fixed tissue sample; contacting the fixedtissue sample with a specific binding entity capable of binding to thelabile biomarker; and detecting binding of the specific binding entity.

Embodiment 53

The method of embodiment 52, wherein the labile biomarker is selectedfrom the group consisting of a phosphorylated protein, an mRNA, and amiRNA.

The foregoing disclosure of the exemplary embodiments of the presentsubject disclosure has been presented for purposes of illustration anddescription. It is not intended to be exhaustive or to limit the subjectdisclosure to the precise forms disclosed. Many variations andmodifications of the embodiments described herein will be apparent toone of ordinary skill in the art in light of the above disclosure.

Further, in describing representative embodiments of the present subjectdisclosure, the specification may have presented the method and/orprocess of the present subject disclosure as a particular sequence ofsteps. However, to the extent that the method or process does not relyon the particular order of steps set forth herein, the method or processshould not be limited to the particular sequence of steps described. Asone of ordinary skill in the art would appreciate, other sequences ofsteps may be possible. Therefore, the particular order of the steps setforth in the specification should not be construed as limitations on theclaims. In addition, the claims directed to the method and/or process ofthe present subject disclosure should not be limited to the performanceof their steps in the order written, and one skilled in the art canreadily appreciate that the sequences may be varied and still remainwithin the spirit and scope of the present subject disclosure.

1. A method for determining a true diffusivity constant of a porousmaterial comprising: computing a set of experimental time-of-flights(TOFs) from measured acoustic data of acoustic waves, the acoustic waveshaving been detected by an acoustic monitoring device and havingtraveled through the porous material, each experimental TOF of thecomputed set of experimental TOFs indicating the TOF of acoustic wavesthat traveled through a candidate diffusivity point of the porousmaterial at a respective one of a plurality of time points; setting arange of candidate diffusivity constants for the porous material; foreach of the candidate diffusivity constants, simulating a spatialdependence concentration model of an expected concentration of a reagentwithin the porous material for the plurality of time points and for thecandidate diffusivity point, the expected concentration of the reagentbeing a function of time, space and said candidate diffusivity constant;using the simulated spatial dependence concentration model for computinga spatial dependence TOF model for the porous material, the TOF modelassigning, to the candidate diffusivity point for each of the pluralityof time points and for each of the candidate diffusivity constants, arespectively modeled TOF; and determining an error function for thecandidate diffusivity point for each of the plurality of time points andfor each of the candidate diffusivity constants, the error functionbeing indicative of a distance between each of the modeled TOFs assignedto said candidate diffusivity point from a corresponding experimentalTOF, the experimental TOF having been measured by the acousticmonitoring device at the same time point as used for modeling itscorresponding modeled TOF; determining a minimum error function based onthe determined error function for the candidate diffusivity point foreach of the plurality of time points and for each of the candidatediffusivity constants; calculating the true diffusivity constant for theporous material based on the determined minimum error function, whereinthe computation of the spatial dependence TOF model comprising:selecting a first one of the candidate diffusivity constant; calculatingan expected reagent concentration (c_(reagent)) at each of the candidatediffusivity points in the porous material for each of the plurality oftime points in dependence of the selected candidate diffusivityconstant; calculating an integrated reagent concentration (c_(detected))for each of the plurality of time points and for each of the candidatediffusivity constants by integrating the expected reagent concentration(c_(reagent)) calculated for said time point and said candidatediffusivity constant over a radius of the porous material; convertingthe integrated reagent concentration to the respective modeled TOF ofthe spatial dependence TOF model by computing a linear combination of aspeed of the acoustic waves in the porous material prior to diffusionwith the reagent and the speed of the acoustic waves in the reagentbeing free of the porous material; and selecting a next one of thecandidate diffusivity constants and repeating this step and the threeprevious steps for the next selected candidate diffusivity constantuntil a termination criterion is reached.